Q(2) The joint probability distribution of X and Y is given by (2x-y)2 for x =...
1. If the joint probability distribution of X and Y is given by f(x, y) for = 1,2,3; y=0,1,2,3 · 42 2. Referring to Exercise 1, find (a) the marginal distribution of X; (b) the marginal distribution of Y. 3. Referring to Exercises 1 and 2, find (a) The expected value of XY. (b) The expected value of X. (c) The expected value of Y (d) The covariance of X and Y (COV(X, Y)). Round your final answer to 3...
Question 4: Let X and Y be two discrete random variables with the following joint probability distribution (mass) function Pxy(x, y): a) Complete the following probability table: Y 2 f(x)=P(X=x) 1 3 4 0 0 0.08 0.06 0.05 0.02 0.07 0.08 0.06 0.12 0.05 0.03 0.06 0.05 0.04 0.03 0.01 0.02 0.03 0.04 2 3 foy)=P(Y=y) 0.03 b) What is P(X s 2 and YS 3)? c) Find the marginal probability distribution (mass) function of X; [f(x)]. d) Find the...
A joint distribution is given by f(x,y) zero, otherwise Calculate the probability f(x.y) 2(v) g1(xly)-L 32 and this becomes when y 1 Solution: V3 2 2x x-1 A joint distribution is given by f(x,y) zero, otherwise Calculate the probability f(x.y) 2(v) g1(xly)-L 32 and this becomes when y 1 Solution: V3 2 2x x-1
[2.5 points] If two random variables have a joint density given by, f(x, y) = k(3x + 2y) 0 for 0 < x < 2, 0 < y < 1 elsewhere (a) Find k (b) Find the Marginal density of Y. (c) Find E(Y) (d) Find marginal density X. (e) Find the probability, P(X < 1.3). (f) Evaluate fı(x|y); (g) Evaluate fi(x|(0.75))
j osxal, osx+y=1 Q) f(x,y) = 24xy (1) Find PC Y >a) find joint density (111) Marginal density and v=x If u=xty fulu). @ f@) = x x @ EWx) ☺ find the paf of 9 = 1 - 4 oly CX Low (23) f(x, y) = 2x7 e 2x find flylx) WEG (11) Cor (x, y) u(0,0) whese Exu) where U (0,) 64 f 6) = $
Determine the value of c that makesthe function f(x,y) = ce^(-2x-3y) a joint probability densityfunction over the range 0 < x and 0 < y < x Determine the following : a) P(X < 1,Y < 2) b) P(1 < X < 2) c) P(Y > 3) d) P(X < 2, Y < 2) e) E(X) f) E(Y) g) MARGINAL PROBABILITY DISTRIBUTION OF X h) Conditional probability distribution of Y given that X=1 i) E(Y given X = 1) j)...
Q#1 Let X and Y are joint probability functions given by a- f(x, y) = *y*; x = 1, 2, 3; y = 1, 2 b- f(x,y) = 5%; x = 2,4,5; y = 1, 2, 3 Find the marginal probability functions of r.v X&Y also find out if X & Y are independent? Q#2 Let X denotes the number of times a certain numerical control machine will malfunction: 1, 2, or 3times on any given day. Let Y denote...
The discrete random variables X and Y take integer values with joint probability distribution given by f (x,y) = a(y−x+1) 0 ≤ x ≤ y ≤ 2 or =0 otherwise, where a is a constant. 1 Tabulate the distribution and show that a = 0.1. 2 Find the marginal distributions of X and Y. 3 Calculate Cov(X,Y). 4 State, giving a reason, whether X and Y are independent. 5 Calculate E(Y|X = 1).
Suppose the joint probability distribution of two binary random variables X and Y are given as follows. x/y 1 2 0 3/10 0 1 4/10 3/10 X goes along side as 0 and 1, Y goes along top as 1 and 2. a) Show the marginal distribution of X. b) Find entropy H(Y ). c) Find conditional entropy H(X|Y ) and H(Y |X). d) Find mutual information I(X; Y ). e) Find joint entropy H(X, Y ). f) Suppose X...